| Abstract: |
| We study the homogeneous Dirichlet boundary value problem of generalized Laplacian systems with a singular weight which may not be integrable.
Some explicit intervals which correspond to the existence and nonexistence of positive solutions for the system with the finite asymptotic behaviors of the nonlinearities at 0 and infinity are obtained.
We show the relationship between the eigenvalue region and the number of positive solutions under various assumptions on the nonlinearities.
Main tool for the proof is the fixed point theorem on a cone. |
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